Finite Group Databasebeta

← C2×#21456350 #30549637

Subgroups — C2×#21456350 #30549637

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840390C212yesmaximal
2#21456350C2116yesmaximal, direct product factor
3C2×#16840171C214yesmaximal, complemented
4C2×#16840164C212yesmaximal, complemented
5C2×#16840160C212yesmaximal, complemented
6C2×#16839804C212yesmaximal
7C2×#16839800C211yesmaximal, characteristic
8C22×#14519709C211yesmaximal, characteristic
9C2×C61×#405C211yesmaximal, characteristic
10#16840390—28no—
11#16840390C22116yes—
12C2×#14519777C2214yes—
13C2×#14519776—22no—
14C2×#14519769C2214yes—
15C2×#14519768—22no—
16C2×#14519754—24no—
17C2×#14519736C2212yes—
18C22×C4⋊Dic61C2212yes—
19#16840171C22132yescomplemented
20#16840164C22116yescomplemented
21#16840160C22116yescomplemented
22#16839804C22116yes—
23#16839800C2218yes—
24C2×#14519711C2212yes—
25C2×#14519711C2214yes—
26C2×#14519709C2212yes—
27C2×#14519709C2212yes—
28C2×#14519709C2218yes—
29C2×#14519709C2211yescharacteristic
30C2×#14519709C2211yescharacteristic
31C2×#14519709C2214yes—
32C22×M16×C61C2211yescharacteristic
33C23×C8×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C61×#405C2218yes—
36C2×#97×C61C2212yes—
37C2×C4×C8×C61C2212yes—
38C22×Dic122—24no—
39C23×Dic61—22no—
40#14519777—28no—
41#14519777C23116yes—
42#14519776—216no—
43#14519769—28no—
44#14519769C23116yes—
45#14519768—216no—
46#14519754—232no—
47#14519736—24no—
48#14519736C2318yes—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—24no—
51C2×C4⋊Dic61—24no—
52C2×C4⋊Dic61C2314yes—
53C2×C4⋊Dic61C2318yes—
54C2×C4⋊Dic61C2312yes—
55C2×C4⋊Dic61C2312yes—
56C2×#11758196—24no—
57C2×#11758196—24no—
58C2×C22⋊Dic61—22no—
59C2×C4×Dic61—22no—
60#14519711C2318yes—
61#14519711C23116yes—
62#14519709C2318yes—
63#14519709C2318yes—
64#14519709C2314yes—
65#14519709C2314yes—
66#14519709C23116yes—
67C23×C4×C61C2311yescharacteristic
68C2×M16×C61Q818yescomplemented
69C2×M16×C61C2314yes—
70C22×C8×C61Q818yescomplemented
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2312yes—
74C22×C8×C61C2314yes—
75#117×C61D414yes—
76#117×C61C2314yes—
77C2×C4⋊C4×C61D412yes—
78C2×C22⋊C4×C61D412yes—
79C2×C42×C61C2312yes—
80#97×C61C2318yes—
81C4×C8×C61C2318yes—
82C24×C61C2×D411yescharacteristic
83C22×C4×C61C2×D414yes—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D412yes—
86C22×C4×C61C2×Q814yes—
87C22×C4×C61C2×Q814yes—
88C22×C4×C61C2411yescharacteristic
89C22×C4×C61C2412yes—
90C22×Dic61—24no—
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—28no—
94C22×Dic61—84no—
95C2×Dic122—216no—
96C2×Dic122—88no—
97M16×C61C2×Q8116yescomplemented
98C2×C8×C61C2×Q814yes—
99C2×C8×C61C2×Q814yes—
100C2×C8×C61C2×Q818yes—
101C2×C8×C61C2×Q8116yescomplemented
102C2×C8×C61C2412yes—
103C2×C8×C61C2414yes—
104C2×C8×C61C2412yes—
105C4⋊C4×C61C2×D418yes—
106C22⋊C4×C61C2×D418yes—
107C42×C61C2×D414yes—
108C42×C61C2414yes—
109C22⋊Dic61—28no—
110C4⋊Dic61—28no—
111C4⋊Dic61—24no—
112C4⋊Dic61—216no—
113C4⋊Dic61—22no—
114C4⋊Dic61—22no—
115C4⋊Dic61C2418yes—
116C4⋊Dic61C2414yes—
117C4⋊Dic61C2414yes—
118#11758196—216no—
119#11758196—216no—
120C4×Dic61—28no—
121C23×C61—24no—
122C23×C61C4⋊Q814yes—
123C23×C61C22×D412yes—
124C23×C61C22×D411yescharacteristic
125C2×C4×C61—28no—
126C2×C4×C61C4⋊Q818yes—
127C2×C4×C61C4⋊Q814yes—
128C2×C4×C61C22×D418yes—
129C2×C4×C61C22×D412yes—
130C2×C4×C61C22×D411yescharacteristic
131C2×C4×C61C22×Q812yes—
132C2×C4×C61C22×Q812yes—
133C2×C4×C61C22×Q814yes—
134C2×C4×C61C22×Q814yes—
135C2×C4×C61C2511yescharacteristic
136C2×Dic61—24no—
137C2×Dic61—24no—
138C2×Dic61—28no—
139C2×Dic61—44no—
140C2×Dic61—48no—
141C2×Dic61—44no—
142C2×Dic61—88no—
143Dic122—816no—
144C8×C61C22×Q814yes—
145C8×C61C22×Q814yes—
146C8×C61C22×Q818yes—
147C2×#3163—611nomaximal, Sylow
148C22×C61—28no—
149C22×C61—24no—
150C22×C61C2×C4⋊Q814yes—
151C22×C61C2×C4⋊Q812yes—
152C22×C61#57714yes—
153C22×C61C23×D411yescharacteristic
154C4×C61—28no—
155C4×C61C2×C4⋊Q814yes—
156C4×C61C2×C4⋊Q812yes—
157C4×C61C23×Q811yescharacteristic
158C4×C61C23×Q811yescharacteristic
159Dic61—44no—
160Dic61—48no—
161Dic61—44no—
162C2×#544—612no—
163#3163—6116no—
164C2×#501—614no—
165C2×#499—612no—
166C2×#498—612no—
167C2×#428—612no—
168C2×#427—611no—
169C22×#106—611no—
170C2×#405D6111yescharacteristic
171C2×C61—24no—
172C2×C61#316314yescomplemented
173C2×C61C22×C4⋊Q811yescharacteristic
174C2×C61C2×#57712yes—
175C22×M16C2×D6111yescharacteristic
176C23×C8C2×D6111yescharacteristic
177#544—6116no—
178#544—1228no—
179C2×C4⋊Q8—614no—
180C2×C4⋊Q8—1222no—
181C2×#125—614no—
182C2×#125—1222no—
183C2×C22⋊Q8—1224no—
184C2×#117—612no—
185C2×#117C2×D6111yescharacteristic
186C22×C4⋊C4—612no—
187#501—6132no—
188#499—6116no—
189#498—6116no—
190#428—6116no—
191#427—618no—
192C2×#107—614no—
193C2×#107—612no—
194C2×#106—611no—
195C2×#106—612no—
196C2×#106—614no—
197C2×#106—611no—
198C2×#106—612no—
199C2×#106—618no—
200#405C2×D6118yes—
201C2×#97C2×D6112yes—
202C2×C4×C8C2×D6112yes—
203C61C2×#316311yescharacteristic, complemented, Sylow
204C22×Q8—1224no—
205C23×C4—1222no—
206C23×C4C22×D6111yescharacteristic
207C2×M16Dic12218yescomplemented
208C2×M16C22×D6114yes—
209C22×C8Dic12218yescomplemented
210C22×C8C22×D6111yescharacteristic
211C22×C8C22×D6111yescharacteristic
212C22×C8C22×D6112yes—
213C22×C8C22×D6114yes—
214C4⋊Q8—6116no—
215C4⋊Q8—12216no—
216C4⋊Q8—1228no—
217#125—6116no—
218#125—12216no—
219#125—1228no—
220C22⋊Q8—12232no—
221#117—618no—
222#117—1224no—
223#117D24414yes—
224#117C22×D6114yes—
225C2×C4⋊C4—614no—
226C2×C4⋊C4—618no—
227C2×C4⋊C4—612no—
228C2×C4⋊C4—612no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—1224no—
231C2×C4⋊C4—1224no—
232C2×C4⋊C4—1224no—
233C2×C4⋊C4—1224no—
234C2×C4⋊C4D24412yes—
235C2×C22⋊C4—1222no—
236C2×C22⋊C4D24412yes—
237C2×C42—1222no—
238C2×C42C22×D6112yes—
239#107—618no—
240#107—6116no—
241#106—618no—
242#106—618no—
243#106—614no—
244#106—614no—
245#106—6116no—
246#97C22×D6118yes—
247C4×C8C22×D6118yes—
248C24C2×D24411yescharacteristic
249C2×Q8—12216no—
250C2×Q8—4888no—
251C22×C4—1228no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1224no—
255C22×C4—4884no—
256C22×C4C2×Dic12214yes—
257C22×C4C2×Dic12214yes—
258C22×C4C2×D24414yes—
259C22×C4C2×D24412yes—
260C22×C4C2×D24411yescharacteristic
261C22×C4C23×D6112yes—
262C22×C4C23×D6111yescharacteristic
263M16C2×Dic122116yescomplemented
264C2×C8C2×Dic12214yes—
265C2×C8C2×Dic12214yes—
266C2×C8C2×Dic12218yes—
267C2×C8C2×Dic122116yescomplemented
268C2×C8C23×D6112yes—
269C2×C8C23×D6114yes—
270C2×C8C23×D6112yes—
271C4⋊C4—618no—
272C4⋊C4—614no—
273C4⋊C4—614no—
274C4⋊C4—1228no—
275C4⋊C4—1224no—
276C4⋊C4—1222no—
277C4⋊C4—1222no—
278C4⋊C4—12216no—
279C4⋊C4—12216no—
280C4⋊C4—12216no—
281C4⋊C4C2×D24418yes—
282C22⋊C4—1228no—
283C22⋊C4C2×D24418yes—
284C42—1228no—
285C42C2×D24414yes—
286C42C23×D6114yes—
287C23—24no—
288C23#1451977714yes—
289C23C22×D24412yes—
290C23C22×D24411yescharacteristic
291Q8—48816no—
292C2×C4—28no—
293C2×C4—1224no—
294C2×C4—1224no—
295C2×C4—1228no—
296C2×C4—4888no—
297C2×C4—2444no—
298C2×C4—2448no—
299C2×C4—2444no—
300C2×C4#1451977718yes—
301C2×C4#1451977714yes—
302C2×C4C22×D24418yes—
303C2×C4C22×D24412yes—
304C2×C4C22×D24411yescharacteristic
305C2×C4C22×Dic12212yes—
306C2×C4C22×Dic12212yes—
307C2×C4C22×Dic12214yes—
308C2×C4C22×Dic12214yes—
309C2×C4C24×D6111yescharacteristic
310C8C22×Dic12214yes—
311C8C22×Dic12214yes—
312C8C22×Dic12218yes—
313C22—24no—
314C22—28no—
315C22C2×#1451977714yes—
316C22C2×#1451977712yes—
317C22#1684057414yes—
318C22C23×D24411yescharacteristic
319C4—28no—
320C4—2448no—
321C4—2444no—
322C4—2444no—
323C4C2×#1451977714yes—
324C4C2×#1451977712yes—
325C4C23×Dic12211yescharacteristic
326C4C23×Dic12211yescharacteristic
327C2—24no—
328C2#2145635014yesdirect product factor
329C2C22×#1451977711yescharacteristic
330C2C2×#1684057412yes—
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#405C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenterC2×#405D61
hypocenterC61C2×#3163
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21456350C2direct (N × H)
3. C2×#16840171C2semidirect
4. C2×#16840164C2semidirect
5. C2×#16840160C2semidirect
19. #16840171C22semidirect
20. #16840164C22semidirect
21. #16840160C22semidirect
68. C2×M16×C61Q8semidirect
70. C22×C8×C61Q8semidirect
97. M16×C61C2×Q8semidirect
101. C2×C8×C61C2×Q8semidirect
172. C2×C61#3163semidirect
203. C61C2×#3163semidirect
207. C2×M16Dic122semidirect
209. C22×C8Dic122semidirect
263. M16C2×Dic122semidirect
267. C2×C8C2×Dic122semidirect
328. C2#21456350direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168403902
#214563502
C2×#168401712
C2×#168401642
C2×#168401602
C2×#168398042
C2×#168398002
C22×#145197092
C2×C61×#4052
C2×#316361